turkmath.org

The ability to compare random outcomes based on the decision makers’risk preferences is crucial to modeling decision making problemsunder uncertainty. In this talk, we focus on preference relationsbased on the second-order stochastic dominance (SSD) and thewidely-applied risk measure conditional value-at-risk (CVAR). Wereview several optimization problems that feature univariate SSD andCVaR-based relations. For many decision making problems, it may alsobe essential to consider multiple and possibly conflicting stochasticperformance measures. In contrast to the univariate comparisons, sucha multicriteria approach requires specifying preference relationsamong randomvectors,where each dimension of a vector corresponds to a decision criterion.This is usually accomplished by extending the univariate stochasticpreference relations to the multivariate case by utilizingscalarization functions. Incorporating such multivariate preferencerules into optimization models is a fairly recent research area. Inparticular, we present a class of multicriteria optimization problemswith multivariate stochastic benchmarking constraints based on CVaR.We discuss the main computational challenges in solving the problemsof interest, and for finite probability spaces we briefly describethe proposed solution methods.